“We don't have the power to make it happen unless the 41 mean what they say, in which case we can get a discharge petition, and we could get it done,” he said.

He emphasized that there's no immediate plan to push a discharge petition, if only because the bill, which has garnered the support of all but four Democrats, was just introduced this week.

“I don't want to anticipate my strategy, you know, at this point in time,” he said. “But we just introduced the bill. We obviously decided, you know, OK, we're going to move ahead on this. We're not going to wait.”

A discharge petition could come into play if lawmakers fail to move a reauthorization by the deadline.

Business group leaders, who have ramped up efforts to build support for the bank amid a partisan battle, have argued that a short-term extension for Ex-Im could dampen the agency’s ability to make loans.

Boehner has deferred action to House Financial Services Committee Chairman Jeb Hensarling (R-Texas), a critic of the bank.

Hensarling's panel staged a hearing on the issue Wednesday, where Rep. Maxine Waters (D-Calif.), the ranking member, was quick to note that 41 Republicans and 200 Democrats would give any legislation enough support to pass the House.

House Democrats — led by Reps. Denny Heck (Wash.) and Lacy Clay (Mo.) — introduced a bill this week that would extend the bank’s charter for seven years, until 2021, and increase the lending cap to $175 billion.

The White House has offered a five-year extension of the bank’s authority with an exposure limit capped at $160 billion.

Draft legislation by Rep. John Campbell (R-Calif.) would extend the bank’s charter for three years and wind down its cap to $95 billion by 2017.